Mathematical foundations of physical theories, including quantum mechanics, statistical mechanics, general relativity, string theory, and the development of rigorous mathematical frameworks for physics
4 papersThis paper develops new techniques for performing computations within and among wrapped Fukaya categories. Key results include a 'descent' property allowing decomposition of these categories and a proof that they are generated by cocores and linking disks. The authors also present a 'stop removal equals localization' result and a Künneth formula.
This paper proves the automorphy of the symmetric power lifting Sym^n f for all n ≥ 1, where f is a cuspidal Hecke eigenform without complex multiplication. This removes a prior assumption requiring the absence of supercuspidal primes. The proof relies on a new automorphy lifting theorem and a refined "killing ramification" technique.
This paper proves the automorphy of symmetric power liftings for all n ≥ 1 for cuspidal Hecke eigenforms of level 1 and weight k > 2. The result also applies to a more general class of eigenforms, including those associated with semistable elliptic curves, significantly advancing Langlands's functoriality principle.
This paper determines the order of magnitude of low moments of Steinhaus and Rademacher random multiplicative functions, proving Helson's conjecture about better-than-squareroot cancellation in the first moment. This result also disproves counter-conjectures and has implications for limit distribution and large deviations of these functions, leveraging a connection to critical multiplicative chaos.